Rabbits were a common staple food source in Australia until 1950s when the myxoma virus was released which causes the disease myxomatosis.
Rabbits were a depression-era food for Australians and was always considered a poor people's food. Being a pest does give make it popular either, much the same as carp is. Which is a shame, as both make great sources of cheap food.
Quite a contrast with the story
Since their introduction for a spot of recreational hunting, European rabbits have had a devastating effect on the ecology of Australia in general. Hence the Rabbit-Proof Fence, and its corresponding novel and film.
Also our most successful rugby league team’s name was given as a derogatory put down: “Rabbitoh”, which was seen as a poor sales person flogging rabbit meat for money
South Sydney being a poor area, yielded the South Sydney Rabbitohs